Intramolecular [3 + 2] Cycloaddition Reactions of Unsaturated Nitrile

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Intramolecular [3+2] Cycloaddition Reactions of Unsaturated Nitrile Oxides. A Study from the Perspective of Bond Evolution Theory (BET) Abel Idrice Adjieufack, Vincent Liégeois, Ibrahim Mbouombouo Ndassa, Joseph KETCHA-MBADCAM, and Benoît Champagne J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b06711 • Publication Date (Web): 24 Aug 2018 Downloaded from http://pubs.acs.org on August 28, 2018

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The Journal of Physical Chemistry

Intramolecular [3+2] Cycloaddition Reactions of Unsaturated Nitrile Oxides. A Study from the Perspective of Bond Evolution Theory (BET) Abel Idrice Adjieufack ,†,‡ Vincent Liégeois,∗,‡ Ibrahim Ndassa Mboumbouo ,¶ Joseph Ketcha Mbadcam ,† and Benoˆıt Champagne‡ †Physical and Theoretical Chemistry of Laboratory, University of Yaoundé 1, Cameroon. ‡Laboratory of Theoretical Chemistry (LCT) and Namur Institute of Structured Matter (NISM), University of Namur, Rue de Bruxelles, 61, B-5000 Namur, Belgium. ¶Department of Chemistry, High Teacher Training College, University of Yaoundé 1,Cameroon. E-mail: [email protected]

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Abstract The reaction mechanism of the [3 + 2] intramolecular cycloaddition of 3,3-dimethyl2-(prop-2-en-1-yloxy) and (prop-2-en-1-ylsulfanyl) nitrile oxides is analyzed using different DFT functionals with 6-311++G(d,p) basis set. The activation and the reaction energies for the cis and trans pathways are evaluated at the DFT, MP2 and CCSD(T) level of theory as well as their Gibbs free energy counterparts. It has shown that the trans regioisomers are both the thermodynamic and kinetic compounds, in agreement with experimental outcomes. For a deeper understanding of the reaction mechanism, a BET analysis along the reaction channel (trans and cis) has been carried out. This analysis reveals that the lone pair on the nitrogen atom is formed first, then the C-C bond and finally the O-C one. The global mechanism is similar for the two compounds and for the two pathways even if some small differences are observed, for instance in the values of the reaction coordinates of appeareance of the different basins.

Introduction At the begining of 20th century Lewis assigned to a pair of electrons shared by two or more nuclei the concept of chemical bond. 1 Following Lewis’s idea, many quantum theories have been set up in order to understand the structure of matter and to rationalize the chemical reactivity including: valence bond (VB) theory, 2–4 molecular orbital (MO) theory 5 and conceptual density functional theory (CDFT). 6,7 However, the concept of bond formation/breaking along a chemical reaction remains a central preoccupation for chemists. For a deeper understanting of the chemical bond, Richard Bader 8,9 has introduced the quantum chemical topology (QCT), 10 which is based on the study of the topology of molecular scalar field. In that frame, a molecule or a crystal is decomposed into atomic domains commonly called atomic basins. In the QCT approach, a partitioning of the molecular space into subsystems (basins) is achieved by applying the theory of dynamical systems to a local well-defined function, which should carry the chemical information. This represents an alter2


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native to understand and describe chemical reactivity that is based on well-defined physical entities, as electron density, ρ(r), which is mesurable experimentaly due to the progress made in X-ray diffraction 11 and spin-polarized neutron diffraction techniques. 12 Within the QCT formalism, Krokidis et al. 13 have proposed the bonding evolution theory (BET) combining the electronic localization function (ELF) 13–15 and Thom’s Catastrophe Theory (CT) 14,16 to understand the chemical mechanism of organic reactions. 17–26 [3 + 2] cycloaddition (32CA’s) between a three-atom-component (TAC) and ethylene derivatives are among the most important and extensively-studied reactions in organic chemistry. Cycloaddition reactions have received a growing interest this last decade owing to their wide preparative significance in the chemistry of drugs and naturals products. Moreover, they are among the most powerful methods for the construction of complex rings and, in particular, 32CA’s, which constitute an important class of these reactions, offer a convenient one-step route to the construction of various complex five-membered heterocycles. 27 Among these, intramolecular cycloadditions are suitable tools for the efficient assembly of complex molecular structures (fused and bridged). 28 The 32CA reactions of nitrile oxides are well-documented in the literature. These reactions provide an efficient route to the synthesis of isoxazolines, which are versatile intermediates for the synthesis of natural products, as well as biologically and medically active compounds. 29,30 They are also excellent substrates for the synthesis of β-amino acids, 31 C-disaccharides, imino /amino polyols, amino sugars and novel aza-heterocycles. 31,32 The interest for synthetic and theoretical studies on intramolecular 32CA reactions has increased considerably owing to their potentials applications. Mahshid et al. 28 have reported a theoretical investigation with B3LYP exchange-correlation (XC) functional and the 6-31G(d,p) basis set on the regioselectivity of the intramolecular hetero Diels-Alder and 32CA reactions of 2-(vinyloxy)benzaldehyde derivatives through two reactive channels (fused and bridged) in which the most stable transition state results in the fused product. Very recently, Domingo et al. 33 have also studied an intramolecular 32CAs reaction of cyclic nitrones within the Molecular Electron Density

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Theory at the MPWB1K/6-311G(d) computational level. The ELF topological analysis of the asynchronous TSs indicates that along the more favorable fused reaction path, the reaction starts with the formation of the C-O single bond. Yonekawa et al. 34 have investigated experimentally intramolecular [3 + 2] cycloaddition of 2-phenoxybenzonitrile N-oxides to benzene rings, forming the corresponding isoxazolines cis-adduct as single isomer. Other groups 35–37 have carried out experimental intramolecular 32CA reactions of alkene-tethered nitrile oxide that provide variable stereoselectivity in generating bicyclic pyrazolines where the butyl group is either cis or trans to the newly formed pyrazolines ring (see scheme 1).

Scheme 1: Trans and Cis reaction channels of the [3 + 2] cycloaddition of 3,3-dimethyl-2(prop-2-en-1-yloxy) 36 and (prop-2-en-1-ylsulfanyl) 35 nitrile oxides . TS-T(TS-C) denotes the trans (cis) transition state leading to the trans (cis) bicycloadduct. The goal of this paper is to elucidate the electron density reorganization along the reactive pathway of the intramolecular 32 CA studied by Hassner and Dehan 35 and Kim et al. 36 with the aid of the bond evolution theory. Within this theory, the electron density rearrangement and the bonding changes along a reaction path are the key ingredients for characterizing the reaction mechanism. To perform quantitative analyses, BET is combined with the ELF topology and Thom’s catastrophe theory. Motivation and originality of this work include answering the following questions: i) what is the nature of the chemical mechanism along the 4


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reaction pathway, one-step or stepwise? ii) where and how electron density reorganization take place along the reaction pathway? iii) how these electron density rearrangements can be associated with chemical events such as the breaking and/or forming of chemical bonds? iv) which types of catastrophes appear along each reaction pathway during the BET? These questions are central to the understanding of the reaction mechanism of this intramolecular 32CA reaction.

Theoretical Background and Calculations Methods A topological analysis of ELF η(r) along the reaction pathway gives attractors basins (domains) in which the probability is maximal for finding an electron pair. Its definition comes from the Hartree-Fock probability of finding two particles of the same spin σ simultaneously at positions r1 and r2 (P2σσ (r1 , r2 )) which reads: 14 P2σσ (r1 , r2 ) = ρσ (r1 )ρσ (r2 ) − |ρσ1 (r1 , r2 )|2

(1)

where

ρσ1 (r1 , r2 )

=

σ X

Ψ∗i (r1 )Ψi (r2 )

(2)

i

is the σ-spin one-body density matrix of the Hartree-Fock determinant. If a σ-spin electron is already located at position r1 , then the conditional probability of finding a second σ-spin electron at position r2 is obtained by dividing the pair probability P2σσ (r1 , r2 ) by the total σ-spin density at r1 : σσ Pcond (r1 , r2 ) = P2σσ (r1 , r2 )/ρσ (r1 )

|ρσ1 (r1 , r2 )|2 = ρσ (r2 ) − ρσ (r1 )

5


(3)


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The conditional probability has two interesting properties: 1) The conditional probability of finding a second σ-spin electron at the same location as the initial σ-spin electron is zero due σσ (r1 , r1 ) = 0) and 2) the total conditional probability to the Pauli exclusion principle (Pcond R σσ (r1 , r2 ) dr2 = Nσ − 1). equal to the number of σ-spin electrons (Nσ ) minus 1 ( Pcond

To obtain the local contribution to the conditional probability, we perform a Taylor expansion of the spherically averaged conditional pair probability. Its leading term reads:

σσ (r, s) Pcond

1 1 |∇ρσ (r)|2 2 = τσ (r) − s + ... 3 4 ρσ (r) 1 = Dσ (r)s2 + . . . 3

(4)

where s is the radius of a spherical shell around r and τσ (r) is the positive-define kinetic energy density. As pointed out by Becke and Edgecombe, 14 Eq. (4) conveys electron localization information. The smaller the probabiity of finding a second electron of the same spin near a r location, the more localize is the electron at that point. The electron localization is therefore related to the smallness of the Dσ (r) term which is zero in the case of a one-electron system. Unfortunately, while Dσ (r) has a lower bound value of zero for highly localized electron, the quantity has no upper bound value. Becke and Edgecombe has therefore propose an alternative ”electron localization function” (ELF, η(r)) having some desirable features: 1

η(r) = 1+

Dσ (r) 0 (r) Dσ

2

(5)

where

Dσ0 (r) =

2/3 5/3 3 6π 2 ρσ (r) 5

(6)

corresponds to Dσ (r) for a uniform electron gas with spin-density equal to the local value

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of ρσ (r). Defined in this manner, the ELF is a dimensionless quantity between 0 and 1. The upper limit η(r) = 1 corresponds to perfect localisation, whereas η(r) = 0.5 indicates behaviour close to that of a uniform gas with the same density. The basins can be classified into two types: core and valence basins. 15 The valence basins can be monosynaptic, disynaptic, trisynaptic and so on, depending on the number of atomic valence shells. According to Lewis model, the monosynaptic basin, denoted V(A), corresponds to lone pairs while the disynaptic, labelled V(A,B) describes the bonding between nuclei A and B. 13 The ELF analysis along the reaction corresponds to BET, which defines a chemical reaction as a sequence of elementary chemical processes separated by catastrophes. The identification of these catastrophes connecting the ELF structural stability domains (SSDs) along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a chemical transformation. In a chemical transformation three types of catastrophes have been observed: 13 (i) the fold catastrophe, corresponding to the creation or to the annihilation of monosynaptic basins; (ii) the cusp catastrophe, which transforms one critical point into three (and vice versa) such as in the formation or the breaking of a covalent bond; (iii) the elliptic umbilic catastrophe in which the index of a critical point changes by two. All geometry optimizations and energy calculations were performed by using the Gaussian 16 program. 38 The geometries of the reactants and transition state (TS) were fully optimized using density functional theory (DFT) in combination with exchange-correlation functionals, B3LYP, 39 B3LYP(D3), 40 M06-2X, 41 M06-2X(D3), 40 and, ωB97X-D 42 and the 6-311++G (d,p) basis set as well as the MP2 level. 43 In Addition single point energies at the CCSD(T) 44 level of approximation with 6-311++G(d,p) basis set using the MP2 geometries were also performed. The integral equation formalism of the polarizable continuum model (IEF-PCM) developed by Tomasi’s group 45 was used in order to take into account solvent effects (benzene). The stationary points were characterized by vibrational frequency

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calculations in order to verify the number of imaginary frequencies (zero for local minimum and one for TS). The IRC curves 46 were evaluated using the second-order Gonzalez-Schlegel integration method 47,48 in order to confirm that the energy profile is connecting the transition state (TS) to the two minima. The global electron density transfer 49 (GEDT) was computed by the sum of the natural atomic charges (q), obtained by a natural population analysis (NPA) 50–52 of the atoms belonging to each framework (f) at the transition states ; P GEDT = qf . For the topological analysis within the BET theory, the wavefunction was obtained for each point of the IRCs at the ωB97X-D/6-311++G(d,p) level and the ELF analysis was performed by means of the TopMod package 53 considering a cubic grid with step-size smaller than 0.2 bohr. The ELF basin positions are visualized using the DrawMol and DrawProfile codes. 54,55

Results and discussion Thermodynamical and geometrical aspects The Table 1, displays the activation energies for the stationary points involved in the studied intramolecular 32CA reactions (see scheme 1). The CCSD(T) single point energies calculations (here considered as reference) were performed from geometries optimized at MP2 level of approximation. Let’s first consider the case of X=O. According to Table 1, it clearly appears that the trans (TS-T) formation is the most favorable. Indeed, the trans activation energy is lower compared to that of the TS-C by about 1.36 kcal/mol in vacuo and 1.33 kcal/mol in benzene. Therefore, this fluctuation of activation energy in benzene does not affect the regioselectivity found in vacuo. With the B3LYP and M06-2X hybrid functional including 20 and 54 % of Hartree-Fock exchange, the energy difference between the cis and trans [E(cis)-E(trans)] are 1.22 and 0.75 kcal/mol respectively. When including dispersion to these functionals, at B3LYP(D3) 8


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the energy difference decreases by about 0.63 kcal/mol due to a larger decrease of the cis activation energy than the trans one, whereas with M06-2X(D3) the difference remains constant (0.74 kcal/mol). When considering the ωB97X-D functional, which includes range separated Hartree-Fock exchange in addition to London dispersion forces, the difference is above that of B3LYP(D3) and M06-2X(D3) by about 0.27 and 0.12 kcal/mol respectively. Second, for X=S, at the CCSD(T) level of approximation the energy difference increases from 0.19 in vacuo to 0.24 kcal/mol in benzene due to the slightly larger solvatation of reactants compared to TSs. Except this effect of solvent (benzene), almost the same trends observed previously in the case of X=O are also recorded here. The Fig. 1 displays the variation of activation energies of different level of approximation with respect to CCSD(T). According to this figure the activation energies are overestimated whereas the reaction energies are underestimated with the MP2 level of approximation. Contrary to MP2, B3LYP and B3LYP(D3) overestimate the reaction energies while the TSs are underestimated. For the other XC-functionals, they compared very well with respect to CCSD(T) reference value for TSs (especially M06-2X, M06-2X(D3) and ωB97X-D) while larger but still reasonnable discrepencies are observed for the reaction energies. Therefore, we have chosen the ωB97X-D XC-functional to perform the BET analyses. The difference of energy between TS-1T (TS-1C) and TS-2T (TS-2C) is small, so the substitution of oxygen atom by sulfur one has little affect on the activation energies. On the contrary, the cycloadducts are slightly more stable in the case of S than for O with the respect to the reactants by about 3 kcal/mol. Table 2 shows the Gibbs free energy of all species involved in the intramolecular 32CA. Considering the case of X=O, the Gibbs free energies indicate that for all methods the cycloadduct 1T is more stable than the cycloadduct 1C (0.81 kcal/mol lower at ωB97XD level). Similarly, the TS-1T barrier is also lower (0.80 kcal/mol) than TS-1C one. The cycloadduct 1T is therefore both the thermodynamic and kinetic isomer. This is in agreement with experimental outcomes where an adduct 1T was observed in 90 % 36 yield. Similarly for

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

20.12 21.34(1.22) -23.14 -22.25 (0.89)

20.15 20.36 (0.21) -26.53 -25.87 (0.66)

20.40 21.60 (1.20) -23.48 -22.48 (1.00)

20.68 20.95 (0.27) -26.58 -25.74 (0.84)

TS-1T TS-1C 1T 1C

TS-2T TS-2C 2T 2C

TS-1T TS-1C 1T 1C

TS-2T TS-2C 2T 2C

B3LYP


10 18.98 19.21 (0.22) -27.45 -26.46 (1.00)

18.79 19.40 (0.60) -24.40 -23.80 (0.70)

18.54 18.64 (0.10) -27.34 -26.53 (0.80)

18.54 19.13 (0.59) -24.14 -23.56 (0.58)

B3LYP(D3)

MP2

CCSD(T)

20.68 36.46 21.56 21.14 (0.46) 37.73 (1.26) 21.80 (0.24) -36.04 -45.09 -41.47 -34.96 (1.08) -43.53 (1.56) -40.40 (1.08)

20.64 34.30 21.51 21.50 (0.86) 36.35 (2.05) 22.83 (1.33) -32.52 -42.06 -37.64 -31.72 (0.80) -40.48 (1.58) -36.46 (1.18)

20.15 35.82 21.22 20.51 (0.36) 36.96 (1.14) 21.41 (0.19) -36.03 -46.03 -41.32 -35.13 (0.90) -44.69 (1.34) -40.40 (0.93)

20.38 34.36 21.26 21.24 (0.86) 36.35 (1.99) 22.62 (1.36) -32.22 -42.30 -37.27 -31.53 (0.69) -40.85 (1.45) -36.19 (1.09)

M06-2X(D3) ωB97X-D

In Vacuo Case 1: X = O 21.50 21.56 22.23 (0.75) 22.30(0.74) -32.48 -32.39 -31.87 (0.61) -31.77 (0.62) Case 2: X = S 21.38 21.41 21.64 (0.26) 21.68 (0.27) -35.98 -35.91 -35.16 (0.81) -35.10 (0.82) In Benzene Case 1: X = O 21.85 21.91 22.60 (0.75) 22.66 (0.75) -32.62 -32.53 -31.90 (0.72) -31.81 (0.72) Case 2: X = S 21.85 21.88 22.20 (0.35) 22.24 (0.36) -35.99 -35.92 -35.00 (0.99) -34.93 (0.99)

M06-2X

Table 1: Relative electronic energies (kcal/mol) with respect to the reactant energies, for the species involved in the intramolecular 32CA reaction as a function of the method of calculation in vacuo and in benzene. All results were obtained with the 6-311++G(d,p) basis set. In parentheses are given trans-to-cis difference [∆E = E(cis) − E(trans)].

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case 2, cycloadduct 2T is the thermodynamic and kinectic isomer obtained experimentally (67 % 35 yield). Since ωB97X-D has been chosen to perform the BET analyses, we use it as a reference when comparing the Gibbs free energies in Fig. 2. For both cases, M06-2X and M06-2X(D3) Gibbs free energies of activation and of reaction are in good agreement with the ωB97X-D ones while B3LYP (case 1), B3LYP(D3) and MP2 underestimate the activation energies and overestimate the reaction ones.

30

B3LYP B3LYP(D3) M06-2X M06-2X(D3) ωB97X-D MP2

25 20 15 10 5 0 −5

2C

2T

2C

S-

T 2T

S-

T

1C

1T

1C

S-

T 1T

S-

T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: Difference of activation and reaction energies (kcal/mol, in vacuo) with respect to the CCSD(T) values function of the method of calculation.

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12

TS-2T TS-2C 2T 2C

TS-1T TS-1C 1T 1C

TS-2T TS-2C 2T 2C

TS-1T TS-1C 1T 1C

◦

M06-2X(D3) Case 1: X = O 17.53 21.13 -12.05 20.49 23.73 18.30(0.76) 22.36(1.23) -13.63(-1.58) 21.41(0.92) 25.01(1.27) -23.12 -17.95 -17.32 -31.16 -26.69 -22.36(0.76) -17.03(0.92) -17.85(-0.53) -30.37(0.79) -25.65(1.04) Case 2: X = S 17.93 21.87 -13.21 20.81 24.47 18.12(0.18) 21.81(-0.06) -12.40(0.82) 21.20(0.39) 24.54(0.07) -25.84 -21.05 -16.05 -34.13 -29.65 -24.96(0.88) -20.30(0.76) -15.64(0.41) -33.24(0.90) -29.52(0.13)

B3LYP(D3)

◦

M06-2X ∆H ∆S ∆H ∆G◦ Case 1: X = O 19.17 22.54 -11.30 20.43 23.67 20.46(1.29) 23.92(1.38) -11.58(-0.28) 21.35(0.92) 24.95(1.28) -22.09 -17.37 -15.84 -31.25 -26.78 -21.06(1.03) -16.27(1.10) -16.06(-0.22) -30.46(0.79) -25.74(1.04) Case 2: X = S 19.68 23.50 -12.78 20.76 24.33 19.92(0.24) 23.60(0.10) -12.31(0.47) 21.14(0.39) 24.40(0.07) -24.9 -29.85 -15.88 -34.23 -29.83 -24.09(0.81) -29.26(0.59) -15.67(0.21) -33.33(0.90) -29.58(0.25)

◦

B3LYP ∆G◦

-12.29 -11.20(1.08) -15.05 -12.48(2.57)

-10.89 -12.07(-1.19) -14.98 -15.83(-0.85)

-12.00 -10.93(1.07) -14.76 -12.60(2.16)

-10.87 -12.07(-1.21) -14.98 -15.82(-0.85)

∆S

◦

∆G

MP2

-11.43 -12.50(-1.07) -15.00 -15.42(-0.42)

∆S◦

23.58 24.38(0.80) -25.42 -24.61(0.81)

ωB97X-D

-13.10 -13.24(-0.14) -17.73 -18.02(-0.29)

16.39 -13.02 16.40(0.01) -13.82(-0.80) -24.96 -16.51 -23.89(1.07) -16.91(-0.40)

17.79 19.15(1.36) -21.59 -20.25(1.33)

◦

19.51 22.86 -11.24 20.05(0.54) 23.54(0.68) -11.70(-0.46) -34.31 -29.83 -15.02 -33.41(0.90) -29.10(0.73) -14.45(0.57)

19.68 20.43(0.75) -30.71 -29.99(0.72)

12.51 12.28(-0.23) -29.89 -29.93(0.95)

14.38 15.42(1.04) -26.06 -24.85(1.21)

∆H

◦

Table 2: Relative enthalpies (∆H◦ , in kcal/mol), entropies (∆S◦ , in cal/mol.K) and Gibbs free energies (∆G◦ , in kcal/mol) for all stationary points involved in the intramolecular reaction with respect to the reactants, as a function of the method of calculation in benzene at 25◦ C. In parentheses are given trans-to-cis difference of each thermodynamic parameter.

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30

B3LYP B3LYP(D3) M06-2X M06-2X(D3) MP2

25 20 15 10 5 0 −5

2C

2T

S-

T

S-

T

1C

1T

S-

T

S-

T

2C

2T

1C

1T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2: Difference of Gibbs free energy of activation and reaction with respect to the ωB97X-D values (kcal/mol) function of the method of calculation.

For each case of these intramolecular cycloaddition reactions, the ωB97X-D/6-311++G (d,p) optimized TSs structures are represented in Fig. 3 with in brackets the geometrical distances obtained in benzene. For Case 1, the lengths of C−C and C−O forming bonds are 2.063 and 2.052 ˚ A, 2.421 and 2.434 ˚ A respectively for TS-1C and TS-1T. In Case 2, they amount to 2.117 and 2.121 ˚ A, 2.330 and 2.354 ˚ A for TS-1C and TS-1T. From these geometric parameters some conclusions can be drawn: i) The extent of the asynchronicity of the bond formation, evaluated as the difference between the lengths of the bonds being formed in the reaction, ∆l = |d(C4 −C3 )-d(C5 −O1 )|, amounts to 0.36 ˚ A at TS-1C, 0.38 ˚ A at TS-1T, 0.21˚ A at TS-2C, and 0.36 ˚ A at TS-2T. These values indicate that the transition state associated to Case 1 have a stronger asynchronous character than those associated to Case 2. This can

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originate from the difference of atomic volume between the two atoms (oxygen and sulfur), which do not allow the alkene framework to easily interact with nitrile oxide one in order to form the bicycloadduct in the Case 2; ii) Inclusion of solvent effects of benzene in the geometry optimization produces appreciable changes with an increase of ∆l due to the C-O length increasing compared to C-C lengths, which remain practically unchanged.

2.421 [2.446]

2.063 [2.057]

2.434 [2.463]

TS-1C

2.330 [2.343]

2.052 [2.046]

TS-1T

2.354 [2.369]

2.117 [2.115]

TS-2C

2.121 [2.119]

TS-2T

Figure 3: ωB97X-D/6-311++G(d,p) optimized geometries for the TSs involved in these intramolecular 32 CA reaction. Key bond distances in vacuo are indicated. Values in brackets refer to the optimized geometries in benzene.

The polar nature of these intramolecular reactions was evaluated by GEDT 49 at the transition state. For Case 1, the GEDT values amount to 0.25 |e| for TS-1C and, 0.25 |e| for TS-1T while for Case 2, they amount to 0.15 |e| for TS-2C and 0.15 |e| for TS-2T. These GEDT values suggest a polar character of these intramolecular reactions according to Domingo who defined reactions with GEDT values of 0.0 |e| as non-polar processes, while 14


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those with values higher than 0.2 |e| correspond to polar processes. 49

BET Analysis of TS-1T regioisomeric channel of compound 1 The BET study of the TS-1T regioisomeric pathway associated with the 32CA intramolecular reaction indicates that the process takes place along seven structural stability domains (SSD) as we can see in Fig. 4, which represents the populations of the basins involved in the cycloaddition. In the SSD-I, the system shows the topologies of the reactant. Three basins are observed: the disynaptic basin V(C4,C5) found between C4 and C5 atoms with a total population of 3.44 |e|, the disynaptic basin V(N2,C3) found between N2 and C3 atoms with a total population of 6.07 |e| and the V(O1) basin associated to the three O1 oxygen lone pairs integrating to a total of 5.73 |e|. At SSD-II, the population of V(N2,C3) basin drops (to attain 4.77 |e|) due to the formation of a new monosynaptic basin V(N2) (of a population of 1.45 |e|) via a fold-F type catastrophe. In the following domain (SSD-III), we observe the creation of two monosynaptic basins: V(C3) and V(C4) with 0.51 and 0.27 |e| that arise from the simultaneous drop of V(N2,C3) and V(C4,C5) disynaptic basin populations, respectively by means of two fold-F type catastrophes (Fig. 5). These two basins join together in domain IV to form the new disynaptic V(C3,C4) basin, which corresponds to the C3-C4 σ- bond by the means of cusp-C type catastrophe. Then, the V(C3,C4) basin population increases while the V(C4,C5) decreases by 0.11 |e|. In the SSD-V, the population of V(C4,C5) basin drops due the formation of the new monosynaptic V(C5) basin (of a population of 0.12 |e|) by means of fold-F catastrophe. Then, at the end of this domain, the population of V(C3,C4) and V(N2) increase to attain 1.63 and 2.55 |e|, respectively (Fig. 4). In the SSD-VI, a second monosynaptic basin V’(O1) (with a population of 0.38 |e|) appears on the oxygen atom (Fig. 4) due to the drop of the V(O1) basin population. 15



TS-1T 20.0

SSD-I

IV

II

V

SSD-VII

7.00

5.00 0.0 4.00 -10.0 3.00 -20.0

-30.0

IRC

V'(O1)

V(C3)

V(C3,C4)

V(C4)

V(C4,C5)

V(C5)

V(N2)

V(N2,C3)

V(O1)

2.00

1.00

V(O1,C5)

-40.0

15.00

10.00

5.00

0.00

-5.00

0.00 -10.00

IRC coordinate [Bohr AMU1/2] Figure 4: Population (in electrons) evolution of selected basins along the IRC (ωB97X-D/ 6-311++G(d,p)) associated with TS-1T regioisomeric channel together with the potential energy surface along the reaction coordinate.

The V(O1,C5) basin is formed in the VII domain by the merger of V’(O1) (which looses 0.38 |e|) and V(C5) (which looses 0.26 |e|) basins (Fig. 5) by means of another cusp-C type catastrophe. Then, the population of the V(O1,C5) basin rises from 0.73 |e| at the beginning of the VII domain to reach 1.28 |e| at the end of the domain (Fig. 4). 16


Number of electrons

6.00

10.0

Energy [kcal/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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V(O1) V(N2,C3) V(N2)

V(C4,C5)

V(C3) V(C4)

SSD-I (13.55)

SSD-II (1.70)

V’(O1)

V(C5)

SSD-V (-2.71)

SSD-III (-0.34)

V(C3,C4)

SSD-IV (-1.02)

V(O1,C5)

SSD-VI (-3.73)

SSD-VII (-4.06)

Figure 5: ELF basin isosurface for selected points that are representative of each of the SSDs found along the IRC associated with TS-1T regioisomeric channel. See Fig. 4 for the color √ labeling of the basins. Reaction coordinates (Bohr AMU) are given in parentheses.

BET Analysis of TS-2T regioisomeric channel of compound 2 Like the TS-1T regioisomeric channel, we have also conducted the BET study along the TS-2T pathway and eight SSDs have been found for this analysis (see Fig. 6). At SSD-I, the system shows the topologies of the reactant with three basins: the V(C4, C5) basin (3.41 |e|) along the C-C double bond, the V(O1) basin on the oxygen atom lone pairs (5.74 |e|) and one V(C3,N2) basin with 6.08 |e| for the triple N-C bond. In the SSD-II, as in Case 1, the V(N2) monosynaptic basin (1.55 |e|) appears first coming from the drop of the V(N2,C3) (from 5.74 to 4.71 |e|) populations (Fig. 7). On the contrary to TS-1T regioisomeric pathway where the two monosynaptic basins (V(C3) and V(C4)) appear simultaneously in the SSD-III domain, they appears here at SSDIII (V(C3) with 0.39 |e| of population) and SSD-IV (V(C4) with 0.36 |e| of populations), respectively (Fig. 7). In the SSD-V, the two monosynaptic basins on C3 and C4 carbon atoms (Fig. 7) merge

17



TS-2T 20.0

SSD-I

V

II

VII SSD-VIII

7.00

6.00

10.0

0.0 4.00 -10.0 3.00 -20.0

-30.0

IRC

V'(O1)

V(C3)

V(C3,C4)

V(C4)

V(C4,C5)

V(C5)

V(N2)

V(N2,C3)

V(O1)

2.00

1.00

V(O1,C5)

-40.0

15.00

10.00

5.00

0.00

-5.00

0.00 -10.00

IRC coordinate [Bohr AMU1/2] Figure 6: Population (in electrons) evolution of selected basins along the IRC (ωB97XD/6-311++G(d,p)) associated with TS-2T regioisomeric channel together with the potential energy surface along the reaction coordinate.

together in order to generate V(C3,C4) disynaptic basin (1.2 |e|) accounting for the C3-C4 bond formation. The new disynaptic basin V(C3,C4) population reaches 1.55 |e| at the SSD-VI while the V(C4,C5) one drops to due to the creation of another new monosynaptic basin V(C5) (which 18


Number of electrons

5.00

Energy [kcal/mol]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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possesses 0.14 |e|) by mean of fold-F type catastrophe (see Fig. 6). At the SSD-VII, a second monosynaptic V(O1) (with 0.23 |e|) the oxygen atom O1 is created simulatenously with the drop of population of the V(O1) basin. The SSD-VIII corresponds to the formation of V(O1,C5) basin (with a population of 0.77 |e|) from the merger of V(C5) and V’(O1) basins, which illustrates the last topological change (cusp-C catastrophe) along the reaction mechanism (Fig. 7).

V(N2)

V(O1) V(N2,C3)

V(C3)

V(C4)

V(C4,C5)

SSD-I (16.65)

V(C3,C4)

SSD-V (-1.34)

SSD-II (1.67)

SSD-III (-0.34)

SSD-IV (-0.67)

V’(O1)

V(C5)

V(O1,C5)

SSD-VI (-2.33)

SSD-VII (-3.00)

SSD-VIII (-4.00)

Figure 7: ELF basin isosurface for selected points that are representative of each of the SSDs found along the IRC associated with TS-2T regioisomeric channel. See Fig. 4 for the color √ labeling of the basins. Reaction coordinates (Bohr AMU) are given in parentheses.

BET Analysis of TS-1C and TS-2C regioisomeric channels The cis pathways are explored with respect to the topological description of the trans regioisomeric ones. The TS-1C pathway can be described from the topological point of view as a series of seven SSDs like TS-1T (Figs. SI-1 and SI-2 in the supplementary materials). The molecular mechanism is similar: the V(N2) basin appears first, followed by the simulatenous creation of V(C3) and V(C4) basins (SSD-III) leading to the C-C bond formation in SSD-IV 19



domain and finally the V(O1,C5) basin along the O1-C5 bond appears (SSD-VII) from the merger of the V(C5) (appeared in SSD-V) and the V’(O1) (appeared in SSD-VI) basins (Fig. SI-2 in the supplementary materials). The TS-2C pathway can be described along seven SSDs (Figs. SI-3 and SI-4 in the supplementary materials) contrary to eight SSDs recorded for TS-2T. The difference of SSDs domains comes from the creation of V(C3) and V(C4) basins which take place at the same domain (SSD-III) for TS-2C pathway while for the TS-2T pathway, they are created in SSDIII and SSD-IV domains (Fig. 7). Apart from this, the description is the same, the V(C3,C4) disynaptic appears by the merger of the V(C3) and V(C4) basin (SSD-IV). Finally the V(O1,C5) basin is formed (SSD-VII) accounting for the C-O bond formation coming from the union of the V(O1) (created in SSD-V) and V(C5) (created in SSD-VI) basins. In addition to the global topology analysis, we compare the reaction coordinates of the appearance of the basins involved in the formation of the C3-C4 and O1-C5 bonds (Table 3). For all cases, the reaction coordinate of the appearence of the second topological change √ (V(C3) and V(C4)) is almost the same (0.34 Bohr AMU) except for V(C4) for TS-2T as already discussed. For the V(C3,C4) one, both cis and trans pathways for case 1 (X=O) √ √ appear at 1.02 Bohr AMU while for case 2 (X=S), both arise at 1.33-1.36 Bohr AMU. For the V(C5) basin, the reaction coordinates of appeareance are all different and range √ from 2.03 to 2.71 Bohr AMU. Therefore, the difference of reaction coordinate between the appeareances of the V(C3) and V(C5) basins decreases when going from TS-1T to TS1C, TS-2T and TS-2C, in agreement with the asynchronicity criterion (∆l) discussed in the Thermodynamical and geometrical aspects section.

20


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√ Table 3: Reaction Coordinate (Bohr AMU) of the appearance of some selected basins along the IRC together with the asynchronicity criterion (∆l in ˚ A). TS-1T TS-1C TS-2T TS-2C V(C3) V(C4) V(C3,C4)

0.34 0.34 1.02

0.34 0.34 1.02

0.33 0.67 1.33

0.34 0.34 1.36

V(C5) V’(O1) V(O1,C5)

2.71 3.73 4.07

2.38 3.74 4.08

2.33 3.00 4.00

2.03 3.39 3.73

V(C5) - V(C3) ∆l

2.37 0.38

2.04 0.36

2.00 0.36

1.69 0.21

Conclusion The mechanism of the [3 + 2] intramolecular cycloaddition reactions through two regioisomeric pathways (trans and cis) have been studied. Only one transition state was found for each reaction channel implying an one-step mechanism. Analysis of the relative Gibbs free energies indicated that the reaction path associated with the formation of the trans-isomer is thermodynamically and kinetically preferred, in agreement with experimental outcomes. For a deeper understanding of the bond forming/breaking during the chemical reaction mechanism, we have performed the BET analysis along this intramolecular cycloaddition. The reaction mechanism is globaly the same for the four channels and can be summarized as follows, i) the V(N2,C3) basin population drops with the appearance of the V(N2) basin associated to the N lone pair, ii) then, two monosynaptic basins (V(C3) and V(C4)) arise simultaneously (except for TS-2T where there is a small shift in the reaction coordinate) together with a fall of the V(N2,C3) and V(C4,C5) basin populations, iii) these two basins then merge to form the C3-C4 bond, iv) at last, the V(O1,C5) basin is created from the merger of V(C5) and V’(O1) basin formed in the meantime from the drop of V(O1) and V(C4,C5) basin populations. In addition to the small difference observed in the reaction mechanism for TS-2T, the appearance of the different basins occur at slightly different reaction coordinates

21



for the different channels.

Supporting Information • Table S1: Electronic energies (a.u) for the species involved in the intramolecular 32CA reaction as a function of the method of calculation in vacuo and in benzene. All results were obtained with the 6-311++G(d,p) basis set. • Table S2: Enthalpies (H◦ , in a.u), entropies (S◦ , in a.u) and Gibbs free energies (G◦ , in a.u) for all stationary points involved in this intramolecular reaction , as a function of the method of calculation in benzene at 25◦ C. • Figure S1: Population (in electrons) evolution of selected basins along the IRC (ωB97XD/ 6-311++G(d,p)) associated with TS-1C regioisomeric channel together with the potential energy surface along the reaction coordinate. • Figure S2: ELF basin isosurface for selected points that are representative of each of the SSDs found along the IRC associated with TS-1C regioisomeric channel. See √ Figure S1 for the color labeling of the basins. Reaction coordinates (Bohr AMU) are given in parentheses. • Figure S3: Population (in electrons) evolution of selected basins along the IRC (ωB97XD/6-311++G(d,p)) associated with TS-2C regioisomeric channel together with the potential energy surface along the reaction coordinate. • Figure S4: ELF basin isosurface for selected points that are representative of each of the SSDs found along the IRC associated with TS-2C regioisomeric channel. See √ Figure S3 for the color labeling of the basins. Reaction coordinates (Bohr AMU) are given in parentheses.

22


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Acknowledgement A.A.I. thanks the University of Namur (Belgium) for his UNamur-CERUNA PhD Mobility Fellowship. V.L. thanks the Fund for Scientific Research (F.R.S.-FNRS) for his Research Associate position. The calculations were performed on the computating facilities of the ´ ´ Consortium des Equipements de Calcul Intensif (CECI), in particular those of the Plateforme Technologique de Calcul Intensif (PTCI) installed in the University of Namur for which we gratefully acknowledge financial support from the FNRS-FRFC (Conventions 2.4.617.07.F and 2.5020.11) and from the University of Namur.

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Intramolecular [3 + 2] Cycloaddition Reactions of Unsaturated Nitrile

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